A $10-$year maturity bond with par value $$1,000$ makes semiannual coupon payments at a coupon rate of $6\%.($Please write the mathematical formula by which you will get a solution of YTM but you can solve it by using a financial calculator or Excel Calculator.$)$

a$.$ Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is $$980.$

b$.$ Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is $$1,000.$

c$.$ Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is $$1,050.$

d$.$ Which of the above three bonds $($in $($a$),($b$)$ and $($c$))$ is the most profitable?